WASHINGTON - U.S. President Donald Trump and Mexican President Andres Manuel Lopez Obrador are touting an accord to reduce the flow of Central American migrants to the U.S.-Mexico border - a deal that led Trump to suspend threatened tariffs on Mexican exports to the United States. Many Republican lawmakers are expressing relief while Democrats are contesting Trump's claims of victory.

An exultant Trump took victory laps on Twitter: "Everyone very excited about the new deal with Mexico!" "There is now going to be great cooperation between Mexico & the USA, something that didn't exist for decades."

Speaking in Tijuana, Lopez Obrador hailed a trade war averted.

'We celebrate the important agreement because it was a very difficult situation and would have been very awkward applying tariffs to some U.S. products, the same measures, commercial restrictions similar to the ones that would be imposed on Mexican exports,' said Lopez Obrador.

The accord calls for Mexico to better patrol its southern border with Guatemala and to hold asylum-seeking migrants while their cases are heard in the United States.

In a statement, Republican Senate Majority Leader Mitch McConnell said it was "good news ... that U.S. families won't be hit with the price increases that would have resulted from new tariffs on imports from Mexico." McConnell also urged more funds for operations along the U.S.-Mexico border, accusing Democrats of "dragging their heels" and engaging in "political gamesmanship."

Democrats, meanwhile, say Trump's own actions have worsened the migrant crisis and that the deal with Mexico was no masterstroke of White House diplomacy.

Democratic presidential candidate Beto O'Rourke said Trump tried to take more credit than was due.

"The president has completely overblown what he purports to have achieved. These are agreements that Mexico had already made, in some cases, months ago ... By and large, the president achieved nothing except to jeopardize the most important trading relationship that the United States of America has. There are six million jobs in this country that depend on U.S.-Mexico trade," said O'Rourke, spaking on ABC's "This Week" program.

For Central American migrants, a perilous journey to the United States is expected to become even more difficult.

Reyna Vazquez, a Honduran migrant in Mexico, says, the migrants' motivation is not always fully understood.

"Everyone should think about the reasons that cause us to migrate and leave our families, our country and come to another country. Instead of closing doors, they should give us an opportunity to demonstrate that we are people who want a job. The only thing we want is a better future for our children and our families," Vazquez said.

Some, like Josue Arenal, another Honduran migrant in Mexico, say they will not be deterred.

"You can close the border, you can build a thousand walls and a thousand walls will be crossed. By land, by air, they are always going to get in. Donald Trump can do whatever he wants," Arenal said.

Migrant arrivals at the U.S.-Mexico border are surpassing 100,000 a month, including record numbers of families and unaccompanied minors.